Electromagnetic and anisotropic extension of a plethora of well-known solutions describing relativistic compact objects
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ORIGINAL ARTICLE
Electromagnetic and anisotropic extension of a plethora of well-known solutions describing relativistic compact objects K. Komathiraj1 · Ranjan Sharma2
Received: 17 October 2020 / Accepted: 16 November 2020 © Springer Nature B.V. 2020
Abstract We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of solutions is that one can easily switch off the electric and/or anisotropic effects in this formulation. Consequently, we show that a plethora of well known stellar solutions can be identified as sub-class of our class of solutions. We demonstrate that it is possible to express our class of solutions in a simple closed form so as to examine its physical viability for the studies of relativistic compact stars. Keywords Einstein-Maxwell system · Exact solution · Relativistic star · Anisotropy
1 Introduction Exact solutions to Einstein-Maxwell system play a major role in the studies of relativistic compact objects. While the Reissner-Nordström solution uniquely describes the exterior gravitational field of a static spherically isolated object in the presence of an electromagnetic field, a large class of interior solutions are available in the literature which are regular, well behaved and physically meaningful. In the uncharged
B R. Sharma
[email protected] K. Komathiraj [email protected]
1
Department of Mathematical Sciences, Faculty of Applied Sciences, South Eastern University of Sri Lanka, Sammanthurai 3000, Sri Lanka
2
Department of Physics, Cooch Behar Panchanan Barma University, Cooch Behar 736101, West Bengal, India
case, a large class of such exact solutions and their physical viability have been examined by Delgaty and Lake (1998). In the charged case, Ivanov (2002) has compiled different class of exact solutions. In the recent past many new exact solutions have been developed some of which are, in fact, generalizations of many of the well-known solutions. Most of the extensions have generally been done either by incorporating an electromagnetic field or anisotropy or both into the system. The generalized models allow us to study the impacts of charge and/or anisotropy on the gross physical behaviour of a compact star. A prime motivating factor for such a generalization in most of our previous works was to fine-tune the stellar observables like mass and radius. Local anisotropy, as indicated by many investigators in the past, plays a significant role in the studies of relativistic stellar objects (Ruderman 1972; Bowers and Liang 1974; Herrera and Santos 1997). In a recent article, it has been argued that pressure anisotropy cannot be ignored in the studies of relativistic compact stars as it is usually expected to develop by the physical processes inside such ultra-compact stars (Herrera 2020). Incorporation of an electromagnetic field in the studies of astrophysical objects is also well-motiv
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